The question is very awkwardly phrased tbh.
Assuming you know what completing the square is, you end up with
where b is from ax2+bx+c, and d is what corrects it to make the final coefficient equal to c from the unfactorised quadratic.
A perfect square trinomial is basically where d has a value of 0 because the (x+b/2)^2 gives you c when expanded.
So if we complete the square on x2+8x then we end up with
, and expanding that gives us
This means c is 16.
As for determining the value of c, it was found by expanding the completed square is how I'd describe it - but again, weirdly phrased question.
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The bonus is an interesting little pro maths tip of mine so I'll help with that too.
The pro tip of mine is always be on the look out for quadratics - they dont always look apparent.
That is indeed a quadratic, just hiding with
.
So we can rewrite it - let's say P = x^2:
Now we can factorise it as we would any other equation, +7 and -1 give us 6 and -7.
Then all we do is take it back to its original form:
Note this can often be done by inspection, but it helps with more complicated ones and it crops up more and more as things get more complex so its worth keeping an eye out for.
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